TABLE 79.-Of the CONNECTION between the ultimate TRANSVERSE STRENGTH of MATERIALS, and the TENSILE, and CRUSHING STRENGTHS.

NOTE -The values marked * have been calculated from the transverse strengths in col. 4, &c., &c.

70-87)

tions. The sum of all the + errors in col. 6 is 76.95, and of the errors is 70.87, giving an average of (76.95 22 +0.276 per cent. on the 22 experiments: the greatest error was 30 per cent. with Glass, and the greatest 15 per cent. with Cast Iron.

error was

-

(509.) It will be interesting and instructive to observe the effect on the transverse strength, of variations in the Tensile and Crushing strengths:-for instance, if by mixture of metals

or otherwise we could double the value of both strains, no doubt the transverse strength would be doubled also; but the question is, what would be the effect of a given alteration in one of those strains only?

Table 80 has been calculated by the rules in (496), &c., and shows the effect of changing the value of T and C from 7 and 42 tons per square inch respectively (which are nearly the mean strengths of ordinary cast iron) to 14 and 7 tons. Thus if T could be doubled or increased to 14 tons, while C remained at its normal value of 42 tons, the increase in the Transverse strength, as shown by col. 5, would be 63.3 per cent. If, on the other hand, with T at its normal value of 7 tons per square inch, C is reduced to 7 tons also, the transverse strength would be reduced to 4962, or about half its normal value; when, as in (500) and (638), the transverse strength is th of T or C; for by col. 4, 389 x 18 7 tons, &c. A practical example of this is given by Stirling's iron in (939), where it is shown that the effect of Stirling's process is to increase the tensile strength 74 per cent., and the crushing strength 30 per cent., the result being an increase of 60 per cent. in the transverse strength by experiment, and 59 per cent. by calculation with the rules in (496), &c.

=

TABLE 80.-Of the TRANSVERSE STRENGTH of CAST IRON, &c., as affected by varying Tensile and Crushing Strength.

THEORETICAL RULES.

(510.) Theoretical writers have given rules connecting the transverse strain on a beam with the tensile and crushing strength of the material, based on the assumption that the two latter are equal to one another, and that the extensions and compressions under those strains are also equal. This, however, is not true of any material (616) when the strains are very heavy or approach the breaking weight; but with the working loads commonly adopted in practice, say th to rd of the breaking weight, those rules are nearly correct, and become of considerable value. With very heavy strains other rules become necessary, and are given in (323).

(511.) For solid square sections of beams we have the rules:—

(514.) For hollow Rectangular sections:

ƒ × 2 × {D3 × B) – (d3 × b}

W =

3 x 1 x D

W =

f

=

3·1416 × { R3 × R2) – (ri × rn}

the maximum strain per square inch at the extreme upper and lower edges of the section, usually tensile at the lower edge and crushing at the lower one, and in the same terms as W.

W the transverse load in the centre of a beam supported at both ends in lbs., tons, &c., including the weight of the beam itself reduced to an equivalent central load (785).

the internal depth in inches.

D

(519.) We may now give some illustrations of the application of these rules:-Say we have a bar of wrought iron 1 inch square and 1 foot long, and assuming that the maximum strain f shall not exceed 12 tons per square inch,-which, as shown by the Diagram 215, is about the limit of perfect elasticity for both the tensile and compressive strains, we may find the equivalent 12 x 2 = 1 transverse strain W by rule (511), which becomes

24

or = 6667 ton, or 1500 lbs. in the centre.

36

If the bar had been a round one, then R

=

3 x 12

0.5, and ⚫53 3.1416 × 12 × ⚫125 12

= .3927

ton in the centre. Hence the ratio of the strengths of square to round bars is 66673927 = 1.7 to 1.0. This is probably the correct ratio for light strains, and nearly so for all strains with materials whose elasticity is nearly perfect, such as steel and wrought iron, but with cast iron and timber, as shown in (361), (362), the ratio with the breaking weights is more nearly 1.5 to 1.0.

(520.) By col. 6 of Table 66, the working load for a plain bar of wrought iron 1 inch square and 1 foot long = .594 ton in